A typical scenario encountered in wireless communication is that of a transmitting access point wanting to communicate simultaneously with J receiving user terminals over a downlink channel. In order to accommodate simultaneous communication with the J users, whose needs and channel conditions may be very different, the resources of bandwidth and power available for communication must be rationally divided. An efficient and increasingly preferred way of dividing the bandwidth is by means of orthogonal frequency division multiplexing (OFDM), whereby the bandwidth is partitioned into a large number of narrow orthogonal tones. Each user is assigned several, possibly nonadjacent, tones. Each tone is assigned to only one user and hence the signals transmitted to the J users remain orthogonal.
Once the tones have been assigned, the available power to be transmitted has to be allocated. Diverse optimality criteria can be used in order to decide which fraction of the available power is allocated to each of the tones. The most fundamental criterion is the maximization of the region of simultaneous mutual informations, which specifies the set of simultaneous user spectral efficiencies that can be achieved reliably. For ideal Gaussian signals, the power allocation that maximizes the region of simultaneous mutual informations is known to be a form of waterfilling. In practice, however, ideal Gaussian signals cannot be realized. Rather, the signals are modulated using discrete constellations for which an optimum power allocation has not been formulated.